| 权重平衡有向网络下分布式约束优化的连续时间算法设计 |
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| 引用本文： | 朱亚楠,温广辉.权重平衡有向网络下分布式约束优化的连续时间算法设计[J].南京气象学院学报,2020,12(5):549-555. |
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| 作者姓名： | 朱亚楠 温广辉 |
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| 作者单位： | 南京信息工程大学 自动化学院, 南京, 210044,东南大学 数学学院/江苏省网络群体智能重点实验室, 南京, 211189 |
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| 基金项目： | 南京信息工程大学人才启动经费（2020r012）；国防科技创新特区项目（2019） |
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| 摘 要： | 本文研究权重平衡有向网络下分布式约束优化问题的求解，其中网络的全局目标函数是由每个智能体的局部目标函数的和构成，全局的约束是由每个智能体的局部约束的交构成.为了分布式求解该问题的最优解，首先引入智能体的局部共轭函数将其转换为Fenchel对偶问题.其次，从Fenchel对偶问题出发，提出一类基于奇异摄动系统的分布式连续时间算法.在局部目标函数和其梯度分别满足强凸和Lipschitz（李普希兹）连续的情况下，结合凸分析方法和Lyapunov（李雅普诺夫）稳定性理论，结果表明所提算法能够获得原问题和对偶问题的最优值.最后，数值仿真进一步验证了所提算法的有效性.
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| 关 键 词： | 分布式约束优化 权重平衡有向网络 Fenchel 对偶问题 奇异摄动系统 |
| 收稿时间： | 2020/7/1 0:00:00 |
Continuous-time algorithm design for distributed constrained optimization over weight-balanced directed networks |
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| ZHU Yanan and WEN Guanghui.Continuous-time algorithm design for distributed constrained optimization over weight-balanced directed networks[J].Journal of Nanjing Institute of Meteorology,2020,12(5):549-555. |
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| Authors: | ZHU Yanan and WEN Guanghui |
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| Institution: | School of Automation, Nanjing University of Information Science&Technology, Nanjing 210044 and Jiangsu Provincial Key Laboratory of Networked Collective Intelligence, School of Mathematics, Southeast University, Nanjing 211189 |
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| Abstract: | This paper investigates a distributed convex optimization with local constraint sets over weight-balanced directed networks,where the global objective function is described as a sum of some agents'' local objective functions.To solve this problem in a distributed way,the problem is transformed into a Fenchel dual problem by introducing local conjugate functions.Then,for the Fenchel dual problem,a distributed continuous-time algorithm is proposed based on the singular perturbation system.When the local objective functions are strongly convex and their gradients are Lipschitz continuous,it is shown that the primal and dual optimality can be both achieved by using the tools from convex analysis and Lyapunov stability.Finally,simulation results are given to illustrate the effectiveness of the proposed algorithm. |
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| Keywords: | distributed constrained optimization weight-balanced directed networks Fenchel dual problem singular perturbation system |
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